1. Field of the Invention
This invention relates generally to the filtering of electrical signals and, more specifically, to a method and apparatus for the removal of undesirable bands of frequencies from an electrical signal.
2. Description of the Prior Art
In sampled signal systems a continuous wave information signal is repetitively sampled to produce a pulse amplitude modulated (PAM) signal. The spectrum of the PAM signal includes a baseband comprising the spectrum of the original continuous signal and a replica of the baseband signal (sideband) centered about each harmonic of the sampling frequency. The tails of the sidebands tend to extend into the baseband and add to its energy, resulting in aliasing distortion of the baseband signal. This aliasing distortion will be present when the baseband signal is subsequently recovered.
Inasmuch as the aliasing distortion results from the sampling process, the only way of curing this distortion is to prevent its occurring in the first place. The common approach to this is to filter the continuous signal in order to band-limit it to frequencies below the highest frequency of interest, and then to sample the resulting band-limited signal at a frequency (the Nyquist rate) in excess of twice this highest frequency of interest.
A lowpass filter employed as described above must not significantly attenuate wanted frequencies. However, above the highest frequency of interest, it should provide as high an attenuation as possible in order to reduce aliasing as much as possible. Unfortunately, conventional filters which provide steep attenuation (roll-off) with frequency tend to be expensive and bulky. Furthermore, the frequency characteristics of such filters tend to be very sensitive to values of reactive components and changes in value which vary with environmental conditions and age.
It is therefore an object of this invention to reduce the aliasing distortion encountered in sampling a continuous wave signal without employing lowpass conventional filters to shape the signal prior to sampling.
The class of N-path type filters known to the art performs bandpass and band-rejection filtering using sampling techniques. Bandpass filters of this variety tend to have a gradual roll-off compared with bandwidth and, therefore, would not be useful in the present application. The band-rejection type filters can be made to exhibit substantially steeper roll-off. In this type of filter samples of the signal to be filtered are commuted among a plurality of power transmission paths, each including a capacitor in series with a signal source. The typical filter characteristic obtained has transmission notches at every harmonic of the commuting frequency and at DC. If the commuting frequency is made to correspond with the sampling frequency of the system, aliasing reduction could be achieved. The most obvious problem with this filter is the notch at DC which results in the loss of low-frequency components when the signal is reconstructed. This has an adverse effect on noise immunity and envelope delay. Another problem with these filters is that the transmission is flat except at the notches. So if the input signal contains any components just above the sampling frequency, these will produce aliasing distortion. The third problem is that the roll-off of the filter characteristic is dependent on the actual values of capacitors used and, therefore, will exhibit variation with environment and age. It is, therefore, another object of this invention to perform sharp lowpass filtering of a signal in such a manner that the roll-off frequency characteristic will be insensitive to the values of component capacitors.
Yet another object of this invention is to perform lowpass filtering with sharp roll-off in a manner that facilitates manufacture by high density integrated circuit techniques.